Logical proof the universe cannot be infinite
Imagine an empty digital photo, say with resolution of 900x900 pixels and 900 colours. It potentially can hold a picture of every planet, star and galaxy that ever was and will ever be, at any arbitrary given time, from every possible angle, every possible altitude. It can hold every photo and movie frame that was ever taken and will be taken, every scene that was ever seen and will be seen, dreamt or imagined by every human or alien that ever was and will ever be. It can also contain every page of every book that existed, exists, and will ever exist... it potentially contains a picture of anything that was and can ever be, a picture of everything that can possibly be, both in reality or imagination, and yet the number of those pictures is not infinite.
Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?
Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?
Comments (54)
The number of picture tokens is (presumably, but it's your rules) equal to the number of pictured scenes.
But the number of picture types is 900^810000, and therefore eventually less than the number of scenes.
It's like, the natural numbers are infinite, but modulo 12 they are 12. And modulo 900^810000 they are 900^810000.
Funny how so much information woo rests on confusing tokens and types; seeing as they were invented by its patron saint.
No offence, @Zelebg, I always enjoy quoting your last word on panpsychism.
Infinity here refers to the maximum possible number of different or unique things or concepts that can possibly exist, ever. For example, the number of unique human faces is not infinite, or the number of unique living things or beings, or the number of unique actions they can perform, thoughts or feelings they can have, it is not infinite.
Or, in the scale of the universe, the number of unique planets, including everything that happens and will ever happen on them, that number is not infinite. So, I am talking about infinity that actually matters, because infinity that at some point starts to repeat is not true infinity, if you ask me.
How is it eventually less, what scenes are not included within the total number of all the pictures that photo can potentially hold?
...or possibly imagine an empty digital photo, with a resolution of 1x1 pixel and 2 colors.
The question is only, what scenes are not assigned their exclusively own personal picture (type). Some at least will have to share.
Heh, yeah, the logic doesn't seem to scale that way, and that baffles me. I mean, just exactly at what resolution the logic starts to fail, and why there, what does that particular resolution has to do with the universe? I feel there is something profound to be learned here, or not, who knows. Who knows!
Don't understand.
Do we agree this logic with empty photo and all the possible pictures it can hold means there is only a finite number of unique book pages that can be written?
The universe that is the model in our minds can not be, because we cannot list an infinity of things. That does not mean that that which is ontologically real (whatever it is) cannot possibly infinite, though it is of course not possible to imagine what that would mean.
Your "of course" surprises me since I do not know of any other argument or reasoning that even comes close to be as convincing. What convinced you that it is not infinite?
I don't get this. How could a 900x900 pixel image show the entire universe or even a small part of the universe?
Perhaps the best way to explain it is to ask what part of the universe it can not show?
Itself, of course. It could not show itself in full detail.
Irony, no doubt, is lost on you.
What part, what detail could it not show? For example, could it show every single square millimetre of Earth, Moon, Jupiter, and Mars? And so on... could there possibly be a planet in the whole universe whose every single square millimetre it could not show?
What does that have to do with anything I said?
If the frame has an infinite number of pixels then the possible images are even more infinite than the number of pixels. If it is1x1 with 2 colors it can only have 2 possible images.
Your irony is a waste of time until you make clear what your opinion is and explain your reasoning.
Your digital photo is a thing in the universe. It lives in a piece of silicon memory in a computer. We think of software as ethereal or nonphysical, but an electrical engineer can measure the electric charges of the bits in a memory chip. Computer memory is a physical thing and the data stored therein is likewise physical. It requires energy to maintain.
If your photo perfectly images everything in the universe, it must image itself in every detail. You have an infinite regress problem in your thought experiment. All simulation arguments do.
But of course that leads to the refutation of your argument. At some level of detail, we must only approximate the world. You can't perfectly image the image of the universe. You must necessarily omit some level of detail. Likewise you must necessarily omit some level of detail about everything. Just like a movie isn't reality even though we see people moving around. It's one still frame after another, and the retention of our eye/brain system fills in the blanks and creates the illusion of motion.
At best you have an approximation of reality. The interesting parts are everything your approximation fails to capture.
If you would please answer the question: could there possibly be a planet in the whole universe whose every single square millimetre it could not show (and even with arbitrary given magnification / zoom in, that is unlimited detail)?
All of them. The detail of the universe far exceeds what you can represent. You couldn't even fully represent a grain of sand ... for the reason that we don't fully understand a grain of sand. What holds the quarks together? Gluons. Why does that work? Why does the binding energy of the quarks create mass and thereby distort the fabric of spacetime, creating the illusion of gravity? We don't know these things. You don't know these things.
Of course you are right, you can indeed represent a picture of a physical object that's perfect up to the resolving ability of the human eye. But that's not much of a standard. It puts us back in the era before we knew about microbes and the germ theory of disease. There's a lot more to the world than we can see.
The artistic movement of pointilism comes to mind. Your image is only an approximation to a certain level of detail.
It is the other way around, the number of possible images my empty photo or your computer screen can represent far exceeds the possible details of the universe, because any given detail can not only be represented as a photograph, but also as a diagram and also with words written descriptions, in every language too.
Whatever detail there can possibly be, known or unknown, visible or not, as long as it can be described with pictures or words, or whatever symbols and diagrams, there is an empty space on your computer screen waiting and ready to represent it, in more than one way.
So you agree that you can only represent computable phenomena. You can't, for example, solve the Halting problem. But it's not known whether the universe is computable or whether the universe can solve the Halting problem. Some people believe so, but there's no proof, nor is it even clear what would constitute proof.
But how can you be certain there are no levels of detail below the resolution of your [math](900 \times 900)^{900}[/math] universe? After all that's a finite number. It's large by everyday standards, but it's very small compared to Skewes's number, Graham's number, Tree(3), the larger Busy Beaver numbers, and other ginormous (Sean Carroll's word) large positive integers studied by mathematicians and computer scientists.
Those numbers may not have physical existence in terms of planets or molecules. But they have undeniable mathematical existence. Where does mathematics fit in your universe?
What scientific principle limits the universe to only that many distinct states, large though your number may be? Wolfram Alpha gives your number as approximately [math]4.33 \times 10^{5317}[/math]. There are more decimal digits of pi than that. How would you represent them?
And to reiterate my earlier concern; if you can perfectly replicate the universe in your grid, you would need to replicate the grid itself, right? Your grid is a physical thing in the universe. Wouldn't that give you a bit of an infinite regress problem?
Or as William Blake said:
[i]To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour[/i]
https://www.poetryfoundation.org/poems/43650/auguries-of-innocence
I don't see why involve computation/simulation in this. For whatever problem we do not yet know the answer to, your computer screen will be able to represent description of the solution if it exist.
So, I am talking about describable phenomena, and I do not know what is indescribable phenomena or can such thing exist.
Because finite resolution is no limit for the amount of detail or zoom factor, so your monitor can show whole Earth from far away, but it can also zoom in and show microscope images of tiny bacteria from up close, and further down it can show electrons and protons, and whatever else as CGI, as illustration, diagram or other kind of symbolic representation.
This holds true for any past, present and future planet and its every square nanometer we zoom in on. Your monitor can show it all, and then some.
Apparently. :yawn:
:100: :up:
You need to look at the Wiki page I linked on the Halting problem. It's an easily stated problem that no computer can possibly solve. It was discovered by Turing in his famous 1936 paper in which he outlined the notion of computation.
Quoting Zelebg
You, or your cat walking across your keyboard, wrote the following in your OP:
Quoting Zelebg
You are clearly talking about everything that is.
But now you say you are only talking about everything that is describable. By whom? By human beings on earth? Well the number of things that could be verbally described by all the human beings who have ever existed is a very small number compared to the size of your grid. So in that case I would grant your premise.
But please note that you have now entirely changed your claim from saying that your grid can represent everything in the universe, to only that which is "describable," a term you haven't bothered to define. And that switcheroo makes a huge difference.
Quoting Zelebg
Only to the limit of your memory to know what's there. You can zoom in on a map because the map's database already holds the data. All the zoom is doing is giving you a different view of the data that already exists in the computer's memory. Likewise you can only zoom in on detail that you already have in your grid; and the information capacity of your grid is limited.
So I repeat my question. By what scientific principle do you claim that the amount of information in the universe is less than the limited size of your grid?
Quoting Zelebg
Only if you have the data stored first. And you have not demonstrated that the total amount of data in the universe is below the limits of your grid.
After all if you have the entire state of the universe stored in memory (which is impossible, because of the infinite regress problem I've already pointed out), you could use a conventional laptop screen to represent parts of it at any zoom level. You are confusing view resolution with the resolution of your stored data.
You should really think about how zooming into a map actually works. The data has to already be there in order for the screen to give you that view.
If you go to Google earth or Google maps and keep zooming in, what happens? Eventually you can't zoom in any more. Why not? Because you've reached the limit of the data that they store. Your viewer would have the same problem. You can only zoom in to the limits of the data you store.
The OP essentially assumes the conclusion, then attempts to "prove" it. :roll:
What a finite resolution image can potentially show has nothing to do with computers and memory limitations.
It's a simple logic exercise. There is no planet in the universe that your monitor could not show a photograph of, from far away, down to every single square nanometre of it. And since finite resolution monitor can only show finite number of different screens, it means the number of unique planets in the universe cannot be infinite.
If this one point is not yet clear, I'm afraid any further discussion is pointless.
This is bad logic. What you can see on your monitor with the naked eye is not all there is. You are saying that we can see only so many different things with the resolution of our eye, and that the number of distinct things we can perceive is relatively small. I agree with that. Then you are concluding that there can be nothing else.
In other words consider two distinct objects that look the same to the naked eye. You are claiming they are not distinct objects. That's bad logic. All you've shown is that the resolution of our naked eyes isn't very good. Please think of the great Antonie van Leeuwenhoek, the first person to see microbes. In your world they don't exist, simply because our feeble eyes can't resolve them. Clearly you are mistaken and making a very elementary error of logic.
Quoting Zelebg
I've stated my points to my satisfaction. Nice chatting with you. I always appreciate the opportunity to mention Skewes's number under any circumstances. All the best.
Uhhh. Empty assertion without explanation, wonderful. Let me break it down...
1. Premise:
There is no planet in the universe that your monitor could not show a photograph of, from far away, down to every single square nanometre of it.
True or false?
2. Conclusion:
And since finite resolution monitor can only show finite number of different screens, it means the number of unique planets in the universe cannot be infinite.
True or false?
Where do you see I am assuming conclusion? I do not. So, then, do you find either premise or conclusion false?
It's beside the point. It's like you are refusing to acknowledge it just because you do not like it, for some strange reason.
I said down to nanometre, and explained previously zoom in can be arbitrarily small. In any case it cannot be "bad logic" since your objection is not about logic but granularity, and to address that I only need to unnecessarily state it more precisely, like so: - it means the number of unique planets (at granularity of one nanometre) in the universe cannot be infinite.
It's not possible for zoom to be arbitrarily small because your computer can't hold that much data. Try arbitrarily zooming into Google maps and you'll see that it's limited by the available data.
Again, what a finite resolution image can potentially show has nothing to do with computers and memory limitations.
LOL. Perhaps I'm not understanding you, because you couldn't possibly believe what you wrote. Your screen can't show data that the computer doesn't know about. Your computer only has a finite amount of data. You can't render anything on the screen below that level, because you haven't got the data. This is a very elementary point.
Just explain to me in simple terms how a computer display can render data that it doesn't have in its memory.
It's about digital image and number of pixel combinations, number of unique pictures the grid can possibly, theoretically, represent. I did open the thread by talking about digital photo, and only later mentioned computer screen, but just as an example of a finite resolution digital image. It has nothing to do with computers, software or memory, it is purely hypothetical scenario exercise in only math and logic.
You can't render data you haven't got. You haven't demonstrated that you have all the data in the universe, or that all the data in the universe is finite, or that even if it is, you have enough storage to hold it. I think if you would carefully write down your argument you'd see that it fails.
I do think we're talking past each other at this point. I can only urge you to clarify your ideas. You have claimed you can zoom arbitrarily. That is not possible if the object of interest represents more data than you can store.
I remember reading and debunking this very same post several years, maybe a decade ago.
Old horse-sticks die hard.
It's also hard to imagine the amount of time and effort I have spent totally in vain trying to tell people precisely why their theories do not hold water. I must have debunked at least a thousand personal pet theories, and the pet theory owners don't mourn over the carcass, because they still believe that their respective beast is still alive.
A bit resembling the Erwin Schrodinger truth: they think the pet is alive and well, while the pet is completely dead.
Stupid.
Retard.
Moron.
:rofl:
Don't blame us for finding the fault in your thinking.
Quoting fishfry
You prefer that to mine? How so?
My reasoning was, the first pixel can be any of 900 distinct (picture-distinguishing) colours, and for each of those (900 mutually exclusive classes of possible picture types) there are 900 choices of colour for the second pixel, so 900 to power 2 is the number, so far, of distinct picture types. Raise the power by one for each of the remainder of the 900 × 900 pixels.
Perhaps you were concerned with something other than the number of possible picture types?
Who would think its infinite?
Everything within the matter of the big bang is what makes our universe, but it being the only universe is another story as space itself can -for now- be infinite.
A grenade does not have infinite amount of shrapnel.
Zelebg
626
Imagine an empty digital photo, say with resolution of 900x900 pixels and 900 colours. It potentially can hold a picture of every planet, star and galaxy that ever was and will ever be, at any arbitrary given time, from every possible angle, every possible altitude. It can hold every photo and movie frame that was ever taken and will be taken, every scene that was ever seen and will be seen, dreamt or imagined by every human or alien that ever was and will ever be. It can also contain every page of every book that existed, exists, and will ever exist... it potentially contains a picture of anything that was and can ever be, a picture of everything that can possibly be, both in reality or imagination, and yet the number of those pictures is not infinite.
Therefore, the universe, along with the number of things, actions, or concepts, is not, and cannot be infinite, not even potentially. Right?
Wrong.
A picture is not the thing itself. A picture of an apple will not satisfy hunger.
You're right, I'm wrong.
Quoting Zelebg
1. You're assuming that such a photo can be taken i.e. you're begging the question.
2. Take an everyday photograph, say, of mount Fuji. Obviously, you won't be able to focus on every single blade of grass that can be found on its slopes. In other words, details are missing and we all know the devil is in the details. Put simply, the photograph of mount Fuji will contain less information than mount Fuji. Same goes for every photograph - the finitude of a photograph doesn't entail the finitude of that which is being photgraphed.